Polarization demultiplexing of optical signals

ABSTRACT

An example embodiment includes optical receiver that includes a polarization beam splitter (PBS), a polarization controller, and a forward error correction (FEC). The PBS is configured to split a received optical signal having an unknown polarization state into two orthogonal polarizations (x′-polarization and y′-polarization). The polarization controller includes no more than two couplers and no more than two phase shifters per wavelength channel of the x′-polarization and the y′-polarization. The polarization controller is configured to demultiplex the x′-polarization and the y′-polarization into a first demultiplexed signal having an first polarization on which a data signal is modulated and a second demultiplexed signal having a second, orthogonal polarization on which a pilot carrier oscillator signal is encoded. The FEC decoder module is configured to correct a burst of errors resulting from resetting one of the phase shifters based on error correction code (ECC) data encoded in the data signal.

RELATED APPLICATION

This application is a continuation of application Ser. No. 14/527,349,filed Oct. 29, 2014, titled POLARIZATION DEMULTIPLEXING OF OPTICALSIGNALS, which claims priority to and the benefit of U.S. ProvisionalApplication No. 61/897,147, both are incorporated herein by reference intheir entirety.

FIELD

The embodiments discussed herein are related to polarizationdemultiplexing of optical signals. In particular, some embodimentsrelate to polarization demultiplexing in pilot carrier singlepolarization quadrature phase shift keying optical signals.

SUMMARY

This Summary is provided to introduce a selection of concepts in asimplified form that are further described below. This Summary is notintended to identify key features of the claimed subject matter, nor isit intended to be used as an aid in determining the scope of the claimedsubject matter.

An example embodiment includes optical receiver. The optical receiverincludes a polarization beam splitter (PBS), a polarization controller,and a forward error correction (FEC) module. The PBS is configured tosplit a received optical signal having an unknown polarization stateinto two orthogonal polarizations (x′-polarization and y′-polarization).The polarization controller includes no more than two couplers and nomore than two phase shifters per wavelength channel of thex′-polarization and the y′-polarization. The polarization controller isconfigured to demultiplex the x′-polarization and the y′-polarizationinto a first demultiplexed signal having an first polarization on whicha data signal is modulated and a second demultiplexed signal having asecond polarization that is orthogonal to the first polarization onwhich a pilot carrier oscillator signal is encoded. The FEC decodermodule is configured to correct a burst of errors resulting fromresetting one of the phase shifters based on error correction code (ECC)data encoded in the data signal.

Another example embodiment includes an optical communication link. Theoptical communication link includes an optical transmitter, an opticalreceiver, and a fiber. The optical transmitter includes an FEC encodermodule, a modulator, a laser, a pilot encoder module, and a polarizationbeam combiner. The FEC encoder module is configured to encode ECC dataon a data signal. The modulator is configured to modulate the datasignal onto a first polarization of an optical signal. The pilot encodermodule is configured to encode a pilot carrier oscillator signal onto asecond polarization of the optical signal. The optical receiver includesa PBS, a polarization controller, and an FEC decoder module. The PBS isconfigured to split a received optical signal having an unknownpolarization state into two orthogonal polarizations (x′-polarizationand y′-polarization). The polarization controller includes no more thantwo couplers and no more than two phase shifters. The FEC decoder moduleis configured to correct a burst of errors resulting from resetting oneof the phase shifters based on the ECC data encoded in the data signal.The fiber optically couples the optical transmitter to the opticalreceiver.

Another example embodiment includes method of polarizationdemultiplexing. The method includes splitting a received optical signalhaving an unknown polarization state into two orthogonal polarizations(x′-polarization and y′-polarization). The method includes phaseshifting either the x′-polarization or the y′-polarization according toa first rotation angle. The method includes generating a third signaland a fourth signal, each of the third signal and the fourth signalbeing a combination of a phase shifted first signal and the other of thex′-polarization or the y′-polarization. The method includes phaseshifting the third signal according to a second rotation angle. Themethod includes generating a first demultiplexed signal and a seconddemultiplexed signal, each of the first demultiplexed signal and thesecond demultiplexed signal including a combination of a phase shiftedthird signal and the fourth signal. The method includes outputting thefirst demultiplexed signal and the second demultiplexed signal.

The object and advantages of the embodiments will be realized andachieved at least by the elements, features, and combinationsparticularly pointed out in the claims.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory and arenot restrictive of the invention, as claimed.

BACKGROUND

Dense wavelength division multiplexing (DWDM) may be used to increasebandwidth in optical communication links. In systems implementing DWDM,multiple optical signals may be combined and transmitted on the sameoptical fiber simultaneously. Each of the optical signals has differentwavelengths. In effect, one fiber is transformed into multiple virtualfibers. Communication networks that implement DWDM networks can carrydifferent types of traffic at different speeds.

An example of a communication network that implements DWDM may bereferred to as a metro DWDM communication network. The metro DWDMcommunication network may be installed to serve cities or metropolitanareas. The metro DWDM communication network may communicate datahundreds of kilometers.

In communication networks implementing DWDM such as the metro DWDMcommunication network, chromatic dispersion may occur. Chromaticdispersion may result in pulse broadening and an increase in bit errors,for instance. Chromatic dispersion may result from the physicalproperties of the optical fibers and the optical signals and may act toeffectively slow the feasible baud rate of optical signals.

Optical polarization multiplexing can be used to double the datacapacity of each wavelength channel or to transmit pilot carrieroscillator signals to aid in detection. In systems implementing opticalpolarization multiplexing, optical signal state of polarization (SOP)may be rotated by the fiber birefringence, which may require some formof polarization control or demultiplexing at the receiver. Polarizationdemultiplexing is accomplished using digital signal processingmulti-input multi-output (DSP MIMO) processing in digital coherentreceivers. One type of receiver that performs the polarizationdemultiplexing is referred to as digital coherent receivers. The digitalcoherent receivers use a local oscillator laser, and the DSP MIMO.However, the local oscillator laser increases the cost of the digitalcoherent receivers and the DSP MIMO processing increases the powerdissipation of the transceiver. An efficient scheme for polarizationcontrol/demultiplexing in the optical domain may enable singlepolarization coherent receivers based on pilot carrier with lower costand lower power use.

The subject matter claimed herein is not limited to embodiments thatsolve any disadvantages or that operate only in environments such asthose described above. Rather, this background is only provided toillustrate one example technology area where some embodiments describedherein may be practiced.

BRIEF DESCRIPTION OF THE DRAWINGS

Example embodiments will be described and explained with additionalspecificity and detail through the use of the accompanying drawings inwhich:

FIG. 1 illustrates a block diagram of an example communication link, inwhich some embodiments described herein may be implemented;

FIG. 2A illustrates a block diagram of example polarization controllersthat may be implemented in the communication link of FIG. 1;

FIG. 2B illustrates block diagram of another example polarizationcontrollers that may be implemented in the communication link of FIG. 1;

FIG. 3 illustrates a block diagram of an example wavelength divisionmultiplex polarization controller; and

FIG. 4 is a flowchart of an example method of polarizationdemultiplexing,

all in accordance with at least one embodiment described herein.

DESCRIPTION OF SOME EXAMPLE EMBODIMENTS

Conventional understanding of polarization controllers is that a systemmay include endless polarization control and redundant phase shifters toeliminate errors during the reset of phase shifters. For example, apolarization controller including endless polarization control isdiscussed in Noe et al., Endless Polarization Control Systems forCoherent Optics, J. OF LIGHTWAVE TECH., Vol. 6, No. 7, July 1988, pp.1199-1208, which is herein incorporated by reference in its entirety.However, the redundant phase shifters may increase the insertion loss ofthe system and controlling the redundant phase shifters may increasecomplexity of a control system.

An example embodiment disclosed herein includes an optical receiver thatbreaks with this conventional understanding. The optical receiverincludes a polarization controller with only two phase shifters or onlytwo phase shifters per wavelength channel. The polarization controllershave non-endless polarization control, but can nevertheless providereliable communications by taking advantage of forward error correction(FEC) coding and/or decoding. When one of the two phase shifters resets,a resulting burst of errors is corrected by an FEC decoding module. Theoptical receiver simplifies the optical polarization demultiplexing andreduces insertion losses when compared to polarization controllers withendless polarization control. This and other embodiments are describedherein with reference to the accompanying drawings.

FIG. 1 illustrates a block diagram of an example optical communicationlink (link) 100, in which some embodiments may be implemented. The link100 depicts a single wavelength channel that may be configured tocommunicate data-carrying optical signals (optical signals).

The link 100 depicted in FIG. 1 includes an optical transmitter(transmitter) 102 optically coupled to an optical receiver (receiver)104 via a single mode fiber (SMF) 106. The transmitter 102 may beconfigured to generate the optical signal. In particular the transmitter102 may be configured to modulate a data signal on a first polarizationof the optical signal and to encode a pilot carrier oscillator signal(pilot carrier signal) on a second polarization of the optical signal.

The transmitter 102 depicted in FIG. 1 includes an example of a pilotcarrier single polarization quadrature phase-shift keying (PCSP QPSK)transmitter. Accordingly, the transmitter 102 is configured to generateand transmit the optical signal on which QPSK data is modulated on thefirst polarization and a pilot carrier signal is encoded on the secondpolarization.

In some embodiments, the transmitter 102 may include a higher orderquadrature amplitude modulation (QAM) transmitter (e.g., 8 QAM, 16 QAM,32 QAM, etc.) or configured for another carrier modulation formatincluding, for example, amplitude-shift keying (ASK), phase-shift keying(PSK), frequency-shift keying (FSK), minimum-shift keying (MSK),Gaussian MSK (GMSK), continuous-phase FSK (CPFSK), multiple FSK (MFSK),or another modulation format.

In some QPSK systems, to receive and interpret data from opticalsignals, a local oscillator, such as a local oscillator laser, may beincluded at a receiver (e.g., the receiver 104). The local oscillator isused to mix with the optical signal for coherent detection of the QPSKdata in the optical signal. In the link 100, instead of the localoscillator being included in the receiver 104, a pilot carrier signalmay be encoded in one of two polarizations of the optical signal. Inparticular, the pilot carrier signal may be encoded in the opticalsignal at the transmitter 102.

For example, in the link 100, the transmitter 102 includes a laser 108.The laser 108 may be configured to generate a continuous wave (CW)optical signal, which may be output by the laser 108, which isrepresented in FIG. 1 at 162. Some examples of the laser 108 mightinclude an external cavity laser or a distributed feedback (DFB) laser.

The CW optical signal 162 may be split at a beam splitter 160 into anx-polarization 112 and a y-polarization 110. The x-polarization 112 andthe y-polarization 110 may be defined according to a coordinate systemof the transmitter 102, however, the designation as “x” and “y” are notnecessarily meaningful other than the implication that thex-polarization 112 is substantially orthogonal to the y-polarization110.

A CW pilot carrier signal may be encoded on the y-polarization 110 by apilot encoder module 164. The x-polarization 112 may be communicated toan in-phase and quadrature (IQ) modulator 114 (in FIG. 1 “IQ”). At theIQ modulator 114, two independent electrical tributaries 150A and 150B(in FIG. 1, “I” and “Q”) of non-return-to-zero (NRZ) data are modulatedinto a QPSK optical signal on the x-polarization 112 at the IQ modulator114. In some embodiments, the QPSK signal may include a symbol rate ofabout 28 gigabaud (GBaud) or any other suitable symbol rate.

The transmitter 102 may also include an FEC encoder module 140. The FECencoder module 140 may be configured to encode error-correcting code(ECC) data into one or both of the tributaries 150A and/or 150B of theNRZ data. The ECC data may be used for error correction of the opticalsignal representative of the NRZ data at the receiver 104.

The x-polarization 112, which includes the QPSK signal, may exit the IQmodulator 114 and may be recombined with the y-polarization 110 at apolarization beam combiner 116. The optical signal including they-polarization 110 and the x-polarization 112 may then be communicatedvia the SMF 106 to the receiver 104.

Before the optical signal is received and/or processed by the receiver104, the polarization state of the optical signal may be altered. Forexample, birefringence in the SMF 106 may alter the polarization stateof the optical signal as the optical signal propagates through the SMF106. In some circumstances, a model of fiber birefringence may berepresented by an example fiber birefringence expression:

$U = \begin{pmatrix}{{\cos\left( \frac{\theta}{2} \right)} - {j\; r_{1}{\sin\left( \frac{\theta}{2} \right)}}} & {{- \left( {r_{3} + {j\; r_{2}}} \right)}{\sin\left( \frac{\theta}{2} \right)}} \\{{- \left( {r_{3} + {j\; r_{2}}} \right)}{\sin\left( \frac{\theta}{2} \right)}} & {{\cos\left( \frac{\theta}{2} \right)} - {j\; r_{1}{\sin\left( \frac{\theta}{2} \right)}}}\end{pmatrix}$In the birefringence expression, U is a 2×2 matrix representing thebirefringence experienced in a fiber. The parameter j represents theimaginary number. The parameters r₁, r₂, and r₃ represent components ofa unit Stokes vector r. The parameter θ represents a rotation angleabout the unit Stokes vector. Accordingly, the optical signal receivedby the receiver may include an unknown polarization state.

The receiver 104 and/or one or more components included therein may beconfigured to perform a polarization demultiplexing of the opticalsignal received at the receiver 104 having an unknown polarizationstate.

The receiver 104 includes a polarization beam splitter (PBS) 120. Anexample of the PBS 120 may include a grating. The PBS 120 may beoptically coupled to the SMF 106. The optical signal having the unknownpolarization state exiting the SMF 106 may be separated by the PBS 120into two orthogonal polarizations. The orthogonal polarizations mayinclude an x′-polarization 166A and a y′-polarization 166B. Thex′-polarization 166A and the y′-polarization 166B may be definedaccording to a coordinate system defined in a reference frame of thereceiver 104.

If, hypothetically, there is no birefringence in the SMF 106, then thex′-polarization 166A and the y′-polarization 166B exiting the PBS 120may match the transmitted x-polarization 112 and y-polarization 110 inthe reference frame of the transmitter. However, due to birefringence ofthe SMF 106, the x′-polarization 166A and the y′-polarization 166Boutput of PBS 120 may include some mixtures of the transmittedpolarization states (e.g., the y-polarization 110 and the x-polarization112) after being rotated by the fiber birefringence (e.g. matrix Uabove).

Accordingly, the polarization demultiplexing performed by the receiver104 or components therein may generally receive the x′-polarization 166Aand the y′-polarization 166B and generate a first demultiplexed signal168A and a second demultiplexed signal 168B (generally, demultiplexedsignal 168 or demultiplexed signals 168). The first demultiplexed signal168A and the second demultiplexed signal 168B may be substantiallysimilar the transmitted x-polarization 112 including encoded QPSK signaland y-polarization 110 including the pilot carrier signal. As mentionedabove, the pilot carrier signal may be used in place of a localoscillator implemented in digital coherent receivers.

The receiver 104 includes a polarization controller 118 configured toreceive the x′-polarization 166A and the y′-polarization 166B exitingthe PBS 120. The polarization controller 118 may include an opticalnetwork 138 and one or more phase shifters 126A and 126B (generally,phase shifter 126 or phase shifters 126). In the depicted embodiment,the optical network 138 includes a second phase shifter 126B and acoupling 124 such as a 50/50 splitter. The optical network 138 and theone or more phase shifters 126 may demultiplex the x′-polarization 166Aand the y′-polarization 166B exiting the PBS 120. The polarizationcontroller 118 may then output demultiplexed signals 168.

For example, the polarization controller 118 may include a first phaseshifter 126A and the optical network 138. The polarization controller118 may accordingly include the optical network 138 and the first phaseshifter 126A that act as two stages of polarization rotators forpolarization demultiplexing. Thus, the polarization controller 118 maybe configured to not have endless polarization tracking. Stated anotherway, the polarization controller 118 has non-endless polarizationtracking.

Additionally, the polarization controller 118 may not include redundantphase shifters. For example, in some embodiments, the polarizationcontroller 118 may include only two phase shifters 126A and 126B. Inthese and other embodiments, one of the two phase shifters 126A or 126Bmay be configured to reset and the other of the two phase shifters 126Aor 126B may be configured to not reset. When one of the phase shifters126A or 126B resets, a burst of errors may be communicated through thepolarization controller 118.

By reducing the number of phase shifters 126, the complexity of thepolarization controller 118 and an associated system configured tocontrol the phase shifters 126 (e.g., controller 252 of FIGS. 2A and 2B)may be reduced. For example, by including two phase shifters 126, theassociated system may not require a phase unwinding algorithm. Thereduction in phase shifters 126 may also reduce the insertion losseswhen compared to polarization controllers including four phase shiftersand/or endless polarization tracking.

In some embodiments, the PBS 120, the polarization controller 118, orsome portions thereof may be implemented as a photonic integratedcircuit (PIC) 122. The PIC 122 may be constructed using siliconphotonics, indium phosphide, or any other suitable materials.

The demultiplexed signals 168 output by the polarization controller 118may be communicated to an optical 90-degree hybrid (90-degree hybrid)128. The 90-degree hybrid 128 may communicate in-phase (I) opticalsignals and quadrature (Q) optical signals to one or more p-i-nphotodetectors 130A-130D (generally, PD 130 or PDs 130). The PDs 130 maybe organized into balanced pairs in some embodiments. The PDs 130 mayconvert the optical signals to electrical signals, which may beprocessed by a digital signal processing (DSP) module 132.

The DSP module 132 may be followed by an FEC decoder module 134. The FECdecoder module 134 may be configured to correct bursts of errors duringphase resets of the phase shifters 126 (e.g., the first phase shifter126A). The FEC decoder module 134 may use any suitable FEC code designedfor burst error correction capability. In an example of the receiver104, each phase reset may be about 10 to about 100 times slower than thesymbol (or baud) rate. The FEC decoder module 134 may correct bursts oferrors during phase resets.

Accordingly, in some embodiments of the receiver 104, the polarizationcontroller 118 is configured to have a non-endless tracking. When thephase shifter 126 (e.g., the first phase shifter 126A) resets, a burstof errors may result. The burst of errors is corrected by the FECdecoder module 134. Thus, in these and other embodiments, the receiver104 may be simplified by omitting components such as multiple otherphase shifters, but may still sufficiently communicate the data encodedin the optical signal.

In some embodiments, the link 100 may represent one of multiplewavelength channels that may be multiplexed onto a fiber in a wavelengthdivision multiplex (WDM) system such as a dense wavelength divisionmultiplex (DWDM) system. For example, an implementation of the link 100may include a metro DWDM system. The metro DWDM system may be configuredto communicate the optical signals hundreds of kilometers (km). Inembodiments of the link 100 that are implemented in a metro DWDM system,one or more optical amplifiers may be included to compensate for thefiber transmission losses. For instance, the metro DWDM system maycommunicate the optical signals about 80 to about 100 km in a singleun-amplified link or multiple spans of about 80 to about 100 km may betraversed with optical amplifiers in each span. Multiplexing multiplewavelength channels in the DWDM system may be performed by DWDMequipment such as transmission/multiplexing equipment, reconfigurableoptical add-drop multiplexer (ROADM) or other suitable equipment, alongthe link 100. In some embodiments, the link 100 may also be configuredto reduce chromatic dispersion of the optical signals, which may developas the optical signals are communicated along the link 100. In these andother embodiments, the link 100 may include optical dispersioncompensating fibers, optical dispersion compensating filters. Someadditional details of a WDM system are provided with reference to FIG.3.

FIGS. 2A and 2B illustrate block diagrams of example polarizationcontrollers 200A and 200B that may be implemented in the link 100 ofFIG. 1. Specifically, in some embodiments, the polarization controllers200A or 200B may correspond to the polarization controller 118 discussedwith reference to FIG. 1. The polarization controllers 200A and 200B maybe configured to reduce the insertion losses associated withdemultiplexing an optical signal 250 having an unknown polarizationstate as compared to polarization controllers with endless polarizationcontrol and/or redundant phase shifters. The optical signal 250 maycorrespond to optical signal generated by the transmitter 102 of FIG. 1and communicated via the SMF 106 of FIG. 1, for example.

The optical signal 250 may be communicated to a PBS 202. The PBS 202 mayinclude a 2-D grating coupling, for instance, or any other suitable beamsplitter. The PBS 202 may be coupled to a first waveguide 204 and to asecond waveguide 206. The PBS 202 may output orthogonal polarizations(x′-polarization and y′-polarization). The first and second signals maybe substantially similar to the x′-polarization 166A and they′-polarization 166B described with reference to FIG. 1.

The PBS 202 may output the x′-polarization and the y′-polarization tothe first waveguide 204 and to the second waveguide 206. For example,the x′-polarization may be output to the first waveguide 204 and they′-polarization may be output to the second waveguide 206 or vice versa.

In some embodiments, the x′-polarization or the y′-polarization mayinclude a transverse electric polarization and the other of thex′-polarization or the y′-polarization may include a transverse magneticpolarization. In these and other embodiments, the polarization havingthe transverse magnetic polarization may be communicated to apolarization rotator (PR) 208 that may rotate the polarization to atransverse electric polarization. In some embodiments, both thex′-polarization and the y′-polarization may have transverse electricpolarizations at the first and second waveguides 204 and 206.

The x′-polarization and the y′-polarization may be represented as [X′Y′], which may be referred to as a received signal vector. Anx-polarization (e.g., 112 of FIG. 1) and a y-polarization (e.g., 110 ofFIG. 1) included in a transmitted optical signal and defined inrelationship to a coordinate system of a transmitter may be representedas [X Y], which may be referred to as a transmitted signal vector.

Accordingly, a goal of the polarization controllers 200A and 200B is todemultiplex the received signal vector [X′ Y′] into the transmittedsignal vector [X Y]. Demultiplexing the received signal vector [X′ Y′]may be accomplished in two stages. A first stage may include applying adifferential phase shift using a first phase shifter 210. A second stagemay include using an optical network 222 including two couplers 212 and220, which may include 50/50 splitters or another coupler/mixer, and asecond phase shifter 218. The polarization controllers 200A and 200B areconfigured to perform a first polarization rotation controlled at leastpartially by the first phase shifter 210 and the second polarizationrotation controlled at least partially by the second phase shifter 218.

The action of the first phase shifter 210 may include rotation thereceived signal vector [X′ Y′] and/or the x′-polarization or they′-polarization on the first waveguide 204 according to a first rotationmatrix:

$\begin{pmatrix}e^{{- j}\frac{\phi_{1}}{2}} & 0 \\0 & e^{j\frac{\phi_{1}}{2}}\end{pmatrix}\quad$In the first rotation matrix, e represents Euler's number (i.e., 2.71 .. . ). The parameter j represents the imaginary number (i.e., j²=−1).The variable Φ₁ represents a first phase rotation angle. The first phaserotation angle Φ₁ may be controlled and varied by a controller 252.Generally, the first phase rotation angle Φ₁ may be reset when the phaserotation angle Φ₁ exceeds a range of about 0 to about 2π.

For example, when one end (e.g., 0 or 2π) of the range is exceeded, thefirst phase shifter 210 may be reset to an opposite end of the range.For instance, when the first phase shifter 210 exceeds the range byincreasing above 2π, the first phase shifter 210 may be reset to 0 andwhen the first phase shifter 210 exceeds the range by decreasing below0, the first phase shifter may be reset to 2π. During the reset timeperiod, a burst of errors may result. The burst of errors may result,for instance, due to improperly demultiplexed signals. As discussed withreference to FIG. 1, the burst of errors may be corrected using an FECdecoder module such as the FEC decoder module 134 of FIG. 1.

In some embodiments, the first phase shifter 210 may include a phasemodulator. The phase modulator may be configured to reset at a rate ofabout ten to about one hundred symbol periods, which may minimize theburst of errors resulting from resetting the phase modulator. Again, theburst of errors resulting from resetting the phase modulator may becorrected using the FEC decoder module.

In some embodiments, a first polarization rotation may be implemented byapplying a differential phase shift in the waveguides 204 and 206 toachieve the first rotation matrix shown above. For example, in someembodiments the first polarization rotator may include a structure asdescribed in Möller, Lothar, WDM Polarization Controller in PLCTechnology, IEEE PHOTONICS TECHNOLOGY LETTERS, Vol. 13, No. 6, June2001, which is incorporated herein by reference in its entirety.

Rotatation the received signal vector [X′ Y′] and/or the x′-polarizationor the y′-polarization on the first waveguide 204 according to a firstrotation matrix may generate a phase-shifted first signal. Thephase-shifted first signal may exit the first phase shifter 210 andenter a first coupler 212, which may be included in the optical network222. Additionally, the x′-polarization or the y′-polarization on thesecond waveguide 206 or exiting PR 208 (or amplifier 228 discussedbelow) may enter the first coupler 212.

A vector representing the phase-shifted first signal and thex′-polarization or the y′-polarization received by the first coupler 212may be represented as a first output vector [X″ Y″]. The first coupler212 may include a 2×2, 50/50 splitter. Accordingly, the first coupler212 may receive the phase-shifted first signal and the x′-polarizationor the y′-polarization received by the first coupler 212 and may outputa third signal and a fourth signal. The third signal and the fourthsignal may include some combination phase-shifted first signal and thex′-polarization or the y′-polarization received by the first coupler212. For instance, in embodiments in which the first coupler 212includes the 2×2, 50/50 splitter each of the third signal and the fourthsignal may include 50% of the phase-shifted first signal and 50% thex′-polarization or the y′-polarization received by the first coupler212. The third signal may be output to a third waveguide 214 and thefourth signal may be output to a fourth waveguide 216.

The third signal may be communicated to a second phase shifter 218 whichmay be configured to apply a phase shift. The phase-shifted third signalexiting the second phase shifter 218 and the fourth signal on the fourthwaveguide 216 may be communicated to a second coupler 220. The secondcoupler 220 may output a fifth signal and a sixth signal that are somecombination of the phase-shifted third signal and the fourth signal. Forinstance, in some embodiments, the second coupler 220 may include a 2×2,50/50 splitter. Accordingly, the second coupler 220 may receive thephase-shifted third signal and the fourth signal and may output thefifth signal and the sixth signal, each including 50% of thephase-shifted third signal and 50% of the fourth signal. The fifth andthe sixth signals represent demultiplexed polarizations of the opticalsignal 250 that are substantially similar to the transmitted signalvector [X Y].

A result of the optical network 222 (i.e., the combination of the firstcoupler 212, the second phase shifter 218, and the second coupler 220)may include a rotation the first output vector [X″ Y″] according to asecond rotation matrix:

$\begin{pmatrix}{\cos\left( \frac{\phi_{2}}{2} \right)} & {{- j}\;{\sin\left( \frac{\phi_{2}}{2} \right)}} \\{{- j}\;{\sin\left( \frac{\phi_{2}}{2} \right)}} & {\cos\left( \frac{\phi_{2}}{2} \right)}\end{pmatrix}\quad$As already discussed, the j represents the imaginary number (i.e.,j²=−1). The parameter Φ₂ represents a second phase rotation angle.

The second phase rotation angle Φ₂ may be controlled and varied by thecontroller 252. In some embodiments, the second rotation angle Φ₂ may bekept in a range of about 0 to about π. Accordingly, in these and otherembodiments, the second phase shifter 218 may not be configured toreset. The second phase shifter 218 may include a thermal-optic phaseshifter or a phase modulator.

With combined reference to FIGS. 1-2B, the demultiplexed polarizationsof the optical signal 250 (e.g., the fifth signal and the sixth signalthat exit the second coupler 220) may include or be substantiallyequivalent to the x-polarization 112 and the y-polarization 110.Specifically, the fifth signal may represent the x-polarization 112,which may include a data signal such as the QPSK data modulated thereon.Additionally, the sixth signal may represent the y-polarization 110,which may include the pilot carrier signal encoded thereon. In anexample embodiment, the fifth signal and the sixth signal may becommunicated to, e.g., the 90-degree hybrid 128 of FIG. 1 for furtherprocessing as already described above such that the data encoded on theoptical signals 250 may be received and processed.

In some embodiments, the second phase shift, which may be performed bythe optical network 222, may be applied in a differential fashion toboth waveguides 214 and 216 to achieve the second rotation matrix shownabove.

In some embodiments, the polarization controllers 200A and 200B mayinclude only two phase shifters 210 and 218 (as opposed to more thantwo) and only two couplers 212 and 220 (as opposed to more than two).The two phase shifters 210 and 218 and the two couplers 212 and 220 maybe sufficient to transform any polarization state of the x′-polarizationand/or the y′-polarization to any other polarization state. Thisconfiguration is specifically and explicitly included in someembodiments. This configuration may result in a burst of errors duringphase resets which are corrected using the FEC decoder module 134 asdescribed above.

In some embodiments, the polarization controller 118 may be constructedusing one or more of bulk optics and PIC. For example, the phaseshifters 210 and 218, the couplers 212 and 220, the PBS 202, the PR 208,the waveguides 204, 206, 214, and 216 or some combination thereof may beincluded in a PIC. The PIC may be constructed using silicon photonictechnologies, for instance. Additionally or alternatively, one or moreof the PBS 202, the PR 208, and the waveguides 206 and 204 may beconstructed of bulk optics.

With reference to FIG. 2B, a second polarization controller 200B may besubstantially similar to the first polarization controller 200A asdescribed herein. In addition, the second polarization controller 200B,may include a first semiconductor optical amplifier (SOA) 226 betweenthe PBS 202 and the first phase shifter 210. Additionally oralternatively, the second polarization controller 200B may include asecond SOA 228 between the PR 208 and the first coupler 212. The firstand second SOAs 226 and 228 may be configured to amplify thex′-polarization and the y′-polarization. For example, before thex′-polarization and/or the y′-polarization enters the first phaseshifter 210, the first SOA 226 may amplify the x′-polarization and/orthe y′-polarization. Likewise, before the x′-polarization and/or they′-polarization enters the first coupler 212, the second SOA 228 mayamplify the x′-polarization and/or the y′-polarization.

Additionally, in the second polarization controller 200B, the first andsecond SOAs 226 and 228, the first and second phase shifters 210 and218, the first and second couplers 212 and 202 and waveguidestherebetween may be included in a PIC 230. The PIC 230 may beconstructed using indium phosphide (InP) or other suitable material(s).Additionally, with combined reference to FIGS. 1 and 2B, in someembodiments, the PIC 230 may include the 90-degree hybrid 128 and/or thePDs 130. In these and other embodiments, the PBS 202 and the PR 208 maybe constructed of bulk optics. In some embodiments of the secondpolarization controller 200B, the first and the second phase shifters210 and 218 may include phase modulators. The phase modulators may havesimilar functions as the phase modulators described with respect to FIG.2A.

FIG. 3 illustrates a block diagram of an example WDM polarizationcontroller 300. The WDM polarization controller 300 may be included inand/or be suitable for polarization control in a WDM system (not shown).The WDM system may include multiple links similar to the link 100 ofFIG. 1. In addition to components included in FIG. 1, the WDM system mayinclude a multiplexer configured to multiplex multiple optical signals(e.g., the optical signals of FIG. 1) having differing wavelengths intoa WDM signal 350. The WDM signal 350 is communicated along a SMF (e.g.,the SMF 106 of FIG. 1) or a multi-mode fiber (MMF). Additionally, theWDM system may include a demultiplexer configured to separate the WDMsignal 350 into multiple wavelength channels. After being separated bythe demultiplexer, the data (e.g., QPSK data) on each wavelength channelmay be received and processed. An example WDM system in which the WDMpolarization controller 300 may be implemented may be a DWDM system or ametro DWDM system having one or more DWDM components.

In some embodiments, the WDM signal 350 may include one or morewavelength channels. The wavelength channels may each have a data signal(e.g., QPSK data) modulated on a first polarization and a pilot carriersignal encoded on a second polarization. The first polarization and thesecond polarization may be defined according to a coordinate system of atransmitter, similar to the x-polarization 112 and y-polarization 110discussed elsewhere herein. The WDM signal 350, when received at the WDMpolarization controller 300 may include an unknown polarization state.

The WDM polarization controller 300 may be configured to receive the WDMsignal 350 and perform a polarization demultiplexing of each of thewavelength channels such that the data signal of each of the wavelengthchannels may be interpreted using the pilot carrier signal at a WDMreceiver (not shown, but similar to the receiver 104 of FIG. 1). In theWDM polarization controller 300, the polarization control may benon-endless, thus bursts of errors may occur during reset of one or morewavelength parallel phase shifters (described below). The bursts oferrors may be corrected using an FEC decoder module (e.g., the FECdecoder module 134 of FIG. 1).

The WDM polarization controller 300 may operate similarly to thepolarization controllers 200A and 200B of FIGS. 2A and 2B. For example,a goal of the WDM polarization controller 300 is to demultiplex anx′-polarization and a y′-polarization, which may be defined inaccordance with a coordinate system of a receiver, of each of thewavelength channels into transmitted polarizations x-polarization andy-polarization.

The WDM polarization controller 300 is configured to perform a firstpolarization rotation of each of the wavelength channels controlled byfirst wavelength selectable phase shifters 302A and a secondpolarization rotation of each of the wavelength channels controlled bythe second wavelength selectable phase shifters 302B. In someembodiments, the WDM polarization controller 300 may implementdifferential phase shifting as discussed elsewhere herein.

A difference between the polarization controllers 200A and 200B of FIGS.2A and 2B and the WDM polarization controller 300 is a substitution ofwavelength selectable phase shifters 302A and 302B (generally,wavelength selectable phase shifter 302 or wavelength selectable phaseshifters 302) for the phase shifters 210 and 218 of FIGS. 2A and 2B. Thewavelength selectable phase shifters 302 may be configured to performphase rotations similar to that described with reference to the phaseshifters 210 of FIGS. 2A and 2B or be included in an optical network 328which may perform a phase rotation along with a first coupler 312 and asecond coupler 320 similar to the optical network 222 of FIGS. 2A and2B. The wavelength selectable phase shifters 302 however, are performedon each of the wavelength channels included in the WDM signal 350.

Specifically, in the depicted WDM polarization controller 300 of FIG. 3,the WDM signal 350 having an unknown polarization state may be separatedinto orthogonal polarizations at a PBS 322. The orthogonal polarizationsmay include an x′-polarization and a y′-polarization. Either thex′-polarization or the y′-polarization may be communicated from the PBS322 to a first optical demultiplexer 306A of a first wavelengthselectable phase shifter 302A. The first optical demultiplexer 306A mayseparate the x′-polarization or the y′-polarization output from the PBS322 into wavelength channels (λ₁-λ₄ in FIG. 3). The wavelength channelsmay be communicated through a first array of parallel phase shifters324. The first array of parallel phase shifters 324 may include multipleparallel phase shifters (individually labeled in FIG. 3 as 310A-310D,collectively referred to as parallel phase shifters 310) that may eachreceive one of the wavelength channels. Specifically, a first wavelengthchannel λ₁ may be communicated to a first of the parallel phase shifters310A, a second wavelength channel λ₂ may be communicated to a second ofthe parallel phase shifters 310B, etc.

Each of the parallel phase shifters 310 may be substantially similar tothe first phase shifter 210 of the polarization controllers 200A and200B of FIGS. 2A and 2B. For example, each of the parallel phaseshifters 310A-310D may apply a differential phase shift to each of thereceived wavelength channels. In some embodiments, each of the parallelphase shifters 310 may rotate one of the received wavelength channels bythe first rotation matrix described above. The rotation that resultsfrom the parallel phase shifters 310 may be based on one or more phaserotation angles, which may be controlled and/or varied by a controller(e.g., the controller 252 of FIGS. 2A and 2B).

One or more of the phase rotation angles of the parallel phase shifters310 may be reset when the phase rotation angles exceed a range of about0 to about 2π. For example, when one end of a range of one of the phaserotation angles is exceeded, the parallel phase shifters 310 may bereset to an opposite end of the range. During the reset time period, aburst of errors may result. The burst of errors may result, forinstance, due to improperly demultiplexed signals. As discussed withreference to FIG. 1, the burst of errors may be corrected using an FECdecoder module such as the FEC decoder module 134 of FIG. 1.

Rotation of the wavelength channels may generate phase-shiftedwavelength channels. The phase-shifted wavelength channels may then bemultiplexed by a first optical multiplexer 308A of the first wavelengthselectable phase shifters 302A. The multiplexed, phase-shiftedwavelength channels may proceed to a first coupler 312. The firstcoupler 312 may include a 2×2 50/50 splitter, for instance. The firstcoupler 312 may output two intermediate signals. The two intermediatesignals may include a combination (e.g., 50/50) of the multiplexed,phase-shifted wavelength channels with the x′-polarization or they′-polarization output from the PBS 322 that did not enter the firstoptical demultiplexer 306A.

A first intermediate signal of the two intermediate signal that areoutput from the first coupler 312 may be communicated to a seconddemultiplexer 306B of the second wavelength selectable phase shifters302B. The second demultiplexer 306B may separate the first intermediatesignal output from the first coupler 312 into the multiple wavelengthchannels (λ₁-λ₄ in FIG. 3). The wavelength channels may be communicatedthrough a second array of parallel phase shifters 326.

The second array of parallel phase shifters 326 may include multipleparallel phase shifters (individually, labeled in FIG. 3 as 318A-318D,collectively referred to as second parallel phase shifters 318) that mayeach receive one of the wavelength channels. Specifically, a firstwavelength channel λ₁ may be communicated to a first of the secondparallel phase shifters 318A, a second wavelength channel λ₂ may becommunicated to a second of the second parallel phase shifters 318B,etc.

One or more of the second parallel phase shifters 318A-318D may besubstantially similar to the second phase shifter 218 of thepolarization controllers 200A and 200B of FIGS. 2A and 2B. Each of thesecond parallel phase shifters 318A-318D may apply a phase shift to oneof the wavelength channels. Phase-shifted wavelength channels output bythe second parallel phase shifters 318A-318D may be multiplexed by asecond multiplexer 308B.

The phase-shifted, multiplexed signal exiting the second wavelengthselectable phase shifter 302B and a second intermediate signal of thetwo intermediate signals exiting the first coupler 312 may becommunicated to a second coupler 320. The second coupler 320 may receivethe phase-shifted, multiplexed signal output from the second multiplexer308B and the second intermediate signal output from the first coupler312. The second coupler 320 may output demultiplexed signals 352A and352B. Each of the demultiplexed signals 352A and 352B may include acombination of the phase-shifted, multiplexed signal output from thesecond multiplexer 308B and the second intermediate signal output fromthe first coupler 312. For example, the second coupler 320 may include a2×2, 50/50 splitter. Accordingly, each of the demultiplexed signals 352Aand 352B may include 50% of the phase-shifted, multiplexed signal and50% of the second intermediate signal.

A result of the optical network 328 (i.e., the combination of the firstcoupler 312, the second wavelength selectable phase shifter 302B, andthe second coupler 320) may include rotation of each of the wavelengthchannels according to the second rotation matrix described above. One ormore second phase rotation angles included in the second rotation matrixmay be controlled and varied by a controller (e.g., 252 of FIGS. 2A and2B). In some embodiments, the second rotation angle applied to each ofthe wavelength channels may be kept in a range of about 0 to about π.The demultiplex signals 352A and 352B may include channel wavelengthshaving polarizations that are substantially similar to transmittedpolarizations x-polarization and y-polarization on which data signalsmay be modulated and a pilot carrier signal may be encoded.

The WDM polarization controller 300 of FIG. 3 includes four parallelphase shifters 310 and 318 in each of the wavelength selectable phaseshifters 302. In some embodiments, the wavelength selectable phaseshifters 302 may include more than four or fewer than four parallelphase shifters 310. These embodiments may be implemented in WDM systemsincluding more than four or fewer than four wavelength channels.

FIG. 4 depicts a flowchart of an example method 400 of polarizationdemultiplexing, in accordance with at least one embodiment describedherein. The polarization demultiplexing may be performed on an opticalsignal such as the optical signal discussed elsewhere herein. Forexample, the optical signal may include QPSK data modulated on a firstpolarization and a pilot carrier signal encoded on a secondpolarization. The first polarization and the second polarization may bedefined with respect to a transmitter such as the x-polarization 112 andthe y-polarization of FIG. 1. The first polarization may be orthogonalto the first polarization.

The method 400 may be performed in a communication link such as the link100 of FIG. 1. For example, the method 400 may be performed in someembodiments by the receiver 104 or one or more components includedtherein. The receiver 104 or one or more components included therein mayinclude non-transitory computer-readable medium having stored thereonprogramming code or instructions that are executable by a computingdevice to cause the computing device to perform the method 400 or someportion thereof. Additionally or alternatively, the receiver 104 mayinclude a processor that is configured to execute computer instructionsto cause a computing system to perform or control performance of themethod 400 or some portion thereof. Although illustrated as discreteblocks, various blocks may be divided into additional blocks, combinedinto fewer blocks, or eliminated, depending on the desiredimplementation.

The method 400 may begin at block 402. At block 402, a received opticalsignal having an unknown polarization state may be split into twoorthogonal polarizations (x′-polarization and y′-polarization). Forexample a PBS may split the optical signal having an unknownpolarization state into the x′-polarization and the y′-polarization. Atblock 404 a phase of either the x′-polarization or the y′-polarizationmay be shifted according to a first rotation angle. In some embodiments,shifting the phase of the x′-polarization or the y′-polarization mayinclude differential phase shifting. In some embodiments, the shiftingthe phase of the x′-polarization or the y′-polarization may includerotating the SOP of the x′-polarization or the y′-polarization by afirst rotation matrix. The first rotation matrix may include:

$\begin{pmatrix}e^{{- j}\frac{\phi_{1}}{2}} & 0 \\0 & e^{j\frac{\phi_{1}}{2}}\end{pmatrix};$In the first rotation matrix, e represents Euler's number, j representsthe imaginary number; and Φ₁ represents the first phase rotation angle.

At block 406, a third signal and a fourth signal may be generated. Insome embodiments one or both of the third signal and the fourth signalmay include a combination of a phase shifted first signal and the otherof the x′-polarization or the y′-polarization. For instance if at block404 x′-polarization is phase shifted, then the third signal and thefourth signal may include a combination of the phase shiftedx′-polarization and the y′-polarization. Alternatively, if at block 404y′-polarization is phase shifted, then the third signal and the fourthsignal may include a combination of the phase shifted y′-polarizationand the x′-polarization.

At block 408, a phase of the third signal may be shifted according to asecond rotation angle. In some embodiments, shifting the phase of thethird signal may include differential phase shifting. In someembodiments, shifting the phase of the third signal may include rotatingthe phase shifted first signal by a second rotation matrix. The secondrotation matrix may include:

$\begin{pmatrix}{\cos\left( \frac{\phi_{2}}{2} \right)} & {{- j}\;{\sin\left( \frac{\phi_{2}}{2} \right)}} \\{{- j}\;{\sin\left( \frac{\phi_{2}}{2} \right)}} & {\cos\left( \frac{\phi_{2}}{2} \right)}\end{pmatrix}\quad$In the second rotation matrix, e represents Euler's number, j representsthe imaginary number; and Φ₂ represents the second phase rotation angle.

At block 410, a first demultiplexed signal and a second demultiplexedsignal may be generated. One or both of the first demultiplexed signaland the second demultiplexed signal may include a combination of a phaseshifted third signal and the fourth signal. At block 412, the firstdemultiplexed signal and the second demultiplexed signal may be output.For example, the first demultiplexed signal and the second demultiplexedsignal may be output to a 90 degree hybrid.

At block 414, in response to the first phase rotation angle of a phaseshifter exceeds a range of about 0 to about 2π, the first phase rotationangle may be reset. At block 416 during the resetting, a burst of errorsmay be allowed to result from improperly demultiplexed signals. At block418, the burst of errors may be corrected using FEC processing.

One skilled in the art will appreciate that, for this and otherprocedures and methods disclosed herein, the functions performed in theprocesses and methods may be implemented in differing order.Furthermore, the outlined steps and operations are only provided asexamples, and some of the steps and operations may be optional, combinedinto fewer steps and operations, or expanded into additional steps andoperations without detracting from the disclosed embodiments. Forexample, the method 400 may include separating the x′-polarization orthe y′-polarization into a plurality of wavelength channels. In theseand other embodiments, the phase shifting the x′-polarization or they′-polarization may include phase shifting each of the plurality ofwavelength channels. Additionally or alternatively, the method 400 mayinclude separating the third signal into the plurality of wavelengthchannels. In these and other embodiments, the phase shifting of thethird signal may include phase shifting each of the plurality ofwavelength channels.

The embodiments described herein may include the use of a specialpurpose or general purpose computer including various computer hardwareor software modules, as discussed in greater detail below.

Embodiments described herein may be implemented using computer-readablemedia for carrying or having computer-executable instructions or datastructures stored thereon. Such computer-readable media may be anyavailable media that may be accessed by a general purpose or specialpurpose computer. By way of example, and not limitation, suchcomputer-readable media may comprise non-transitory computer-readablestorage media including RAM, ROM, EEPROM, CD-ROM or other optical diskstorage, magnetic disk storage or other magnetic storage devices, or anyother non-transitory storage medium which may be used to carry or storedesired program code means in the form of computer-executableinstructions or data structures and which may be accessed by a generalpurpose or special purpose computer. Combinations of the above shouldalso be included within the scope of computer-readable media.

Computer-executable instructions comprise, for example, instructions anddata which cause a general purpose computer, special purpose computer,or special purpose processing device to perform a certain function orgroup of functions. Although the subject matter has been described inlanguage specific to structural features and/or methodological acts, itis to be understood that the subject matter defined in the appendedclaims is not necessarily limited to the specific features or actsdescribed above. Rather, the specific features and acts described aboveare disclosed as example forms of implementing the claims.

As used herein, the term “module” or “component” may refer to softwareobjects or routines that execute on the computing system. The differentcomponents, modules, engines, and services described herein may beimplemented as objects or processes that execute on the computing system(e.g., as separate threads). While the system and methods describedherein are preferably implemented in software, implementations inhardware or a combination of software and hardware are also possible andcontemplated. In this description, a “computing entity” may be anycomputing system as previously defined herein, or any module orcombination of modulates running on a computing system.

All examples and conditional language recited herein are intended forpedagogical objects to aid the reader in understanding the invention andthe concepts contributed by the inventor to furthering the art, and areto be construed as being without limitation to such specifically recitedexamples and conditions. Although embodiments of the present inventionshave been described in detail, it should be understood that the variouschanges, substitutions, and alterations could be made hereto withoutdeparting from the spirit and scope of the invention.

What is claimed is:
 1. An optical receiver comprising: a polarizationbeam splitter (PBS) configured to split a received optical signal havingan unknown polarization state into two orthogonal polarizations thatinclude an x′-polarization and a y′-polarization; a polarizationcontroller having non-endless polarization tracking, the polarizationcontroller including only two couplers and only two phase shifters perchannel, a first phase shifter of the two phase shifters beingconfigured to reset when a first phase rotation angle exceeds a range ofabout 0 to about 2π, and a second phase shifter of the two phaseshifters being configured to maintain a second phase rotation anglebetween about 0 and about π; and a forward error correction (FEC)decoder module configured to correct a burst of errors resulting fromresetting one of the two phase shifters based on error correction code(ECC) data encoded in the received optical signal.
 2. The opticalreceiver of claim 1, further comprising a photonic integrated circuit(PIC) that includes the PBS and the polarization controller that isconstructed of silicon photonics or indium phosphide.
 3. The opticalreceiver of claim 1, wherein the polarization controller includes anoptical network that includes the two couplers and the first phaseshifter or the second phase shifter.
 4. The optical receiver of claim 1,further comprising: an optical 90-degree hybrid; and one or more p-i-nphotodetectors, wherein: the polarization controller is configured todemultiplex the x′-polarization and the y′-polarization into a firstdemultiplexed signal having a first and a second demultiplexed signalhaving a second polarization that is orthogonal to the firstpolarization, and the optical 90-degree hybrid receives the firstdemultiplexed signal and the second demultiplexed signal from thepolarization controller.
 5. The optical receiver of claim 4, wherein: adata signal is modulated on the first demultiplexed signal; and a pilotcarrier oscillator signal is encoded on the second demultiplexed signal.6. The optical receiver of claim 5, wherein the data signal modulated onthe first demultiplexed signal includes data modulated using singlepolarization quadrature phase shift keying (QPSK).
 7. The opticalreceiver of claim 1, further comprising one or more semiconductoroptical amplifiers configured to amplify at least one of thex′-polarization or the y′-polarization.
 8. The optical receiver of claim1, wherein the first phase shifter is configured rotate one of thex′-polarization or the y′-polarization by a first rotation matrix:$\begin{pmatrix}e^{{- j}\frac{\phi_{1}}{2}} & 0 \\0 & e^{j\frac{\phi_{1}}{2}}\end{pmatrix};$ in which: e represents Euler's number; j represents theimaginary number; and Φ₁ represents the first phase rotation angle. 9.The optical receiver of claim 8, wherein: a first of the two couplers isconfigured to receive a phase-shifted signal output by the first phaseshifter and the other of the x′-polarization or the y′-polarization andoutput a third signal and a fourth signal; and each of the third signaland the fourth signal include a portion of the phase-shifted signal anda portion the x′-polarization or the y′-polarization that is received bythe first of the two couplers.
 10. The optical receiver of claim 9,wherein the second phase shifter and one or both of the two couplers areconfigured to rotate the phase-shifted signal output by the first phaseshifter according to a second rotation matrix: $\begin{pmatrix}{\cos\left( \frac{\phi_{2}}{2} \right)} & {{- j}\;{\sin\left( \frac{\phi_{2}}{2} \right)}} \\{{- j}\;{\sin\left( \frac{\phi_{2}}{2} \right)}} & {\cos\left( \frac{\phi_{2}}{2} \right)}\end{pmatrix};$ in which Φ₂ represents the second phase rotation angle.11. The optical receiver of claim 1, further comprising: a first opticaldemultiplexer between the PBS and the first phase shifter, wherein thefirst optical demultiplexer is configured to separate thex′-polarization or the y′-polarization output from the PBS into two ormore wavelength channels; a first optical multiplexer between the firstphase shifter and a first coupler of the two couplers, the first opticalmultiplexer being configured to multiplex a phase-shifted wavelengthchannel output from the first phase shifter with one or more otherphase-shifted wavelength channels; a second optical demultiplexerbetween the first coupler and the second phase shifter, wherein thesecond optical demultiplexer is configured to separate a firstintermediate signal output from the first coupler into the two or morewavelength channels; and a second optical multiplexer between the secondphase shifter and a second coupler of the two couplers, the secondoptical multiplexer being configured to multiplex a phase-shiftedwavelength channel output from the second phase shifter with one or moreother phase-shifted wavelength channels.
 12. A polarization controllerthat is configured to have a non-endless polarization tracking and toreceive optical signal having an unknown polarization state, thepolarization controller comprising: only two phase shifters per channel,a first phase shifter of the two phase shifters being configured toreset when a first phase rotation angle exceeds a range of about 0 toabout 27 and a second phase shifter of the two phase shifters beingconfigured to maintain a second phase rotation angle between about 0 andabout π; and only two couplers, wherein: the received optical signalincludes two orthogonal polarizations that include an x′-polarizationand a y′-polarization; the polarization controller is configured todemultiplex the x′-polarization and the y′-polarization into a firstdemultiplexed signal having a first polarization and a seconddemultiplexed signal having a second polarization that is orthogonal tothe first polarization; and during a time period in which the firstphase shifter is reset, the received optical signal propagates throughthe polarization controller with improperly demultiplexed signals thatincludes a burst of errors that is corrected by a forward errorcorrection (FEC) decoder module.
 13. The polarization controller ofclaim 12, further comprising: a polarization beam splitter (PBS) that isconfigured to split the received optical signal into the x′-polarizationand the y′-polarization; a first optical demultiplexer between the PBSand the first phase shifter, wherein the first optical demultiplexer isconfigured to separate the x′-polarization or the y′-polarization outputfrom the PBS into two or more wavelength channels; a first opticalmultiplexer between the first phase shifter and a first coupler of thetwo couplers, the first optical multiplexer being configured tomultiplex a phase-shifted wavelength channel output from the first phaseshifter with one or more other phase-shifted wavelength channels; asecond optical demultiplexer between the first coupler and the secondphase shifter, wherein the second optical demultiplexer is configured toseparate a first intermediate signal output from the first coupler intothe two or more wavelength channels; and a second optical multiplexerbetween the second phase shifter and a second coupler of the twocouplers, the second optical multiplexer being configured to multiplex aphase-shifted wavelength channel output from the second phase shifterwith one or more other phase-shifted wavelength channels.
 14. Thepolarization controller of claim 12, further comprising: a polarizationbeam splitter (PBS) that is configured to split the received opticalsignal into the x′-polarization and the y′-polarization; a firstwaveguide that connects to the PBS, a second waveguide that connects tothe PBS; and a polarization rotator that is positioned between the PBSand a first of the two couplers.
 15. The polarization controller ofclaim 12, further comprising: a polarization beam splitter (PBS) that isconfigured to split the received optical signal into the x′-polarizationand the y′-polarization; a first semiconductor optical amplifier (SOA)that is positioned between the PBS and the first phase shifter; apolarization rotator that is positioned between the PBS and a first ofthe two couplers; and a second SOA that is positioned between thepolarization rotator and the first of the two couplers.
 16. Thepolarization controller of claim 12, wherein the first phase shifter isconfigured rotate one of the x′-polarization or the y′-polarization by afirst rotation matrix: $\begin{pmatrix}e^{{- j}\frac{\phi_{1}}{2}} & 0 \\0 & e^{j\frac{\phi_{1}}{2}}\end{pmatrix};$ in which: e represents Euler's number; j represents theimaginary number; and Φ₁ represents the first phase rotation angle. 17.The polarization controller of claim 16, wherein: a first of the twocouplers is configured to receive a phase-shifted signal output by thefirst phase shifter and the other of the x′-polarization or they′-polarization and output a third signal and a fourth signal; and eachof the third signal and the fourth signal include a portion of thephase-shifted signal and a portion the x′-polarization or they′-polarization that is received by the first of the two couplers. 18.The polarization controller of claim 17, wherein the second phaseshifter and one or both of the two couplers are configured to rotate thephase-shifted signal output by the first phase shifter according to asecond rotation matrix: $\begin{pmatrix}{\cos\left( \frac{\phi_{2}}{2} \right)} & {{- j}\;{\sin\left( \frac{\phi_{2}}{2} \right)}} \\{{- j}\;{\sin\left( \frac{\phi_{2}}{2} \right)}} & {\cos\left( \frac{\phi_{2}}{2} \right)}\end{pmatrix};$ in which Φ₂ represents the second phase rotation angle.19. The polarization controller of claim 12, wherein: one or both of thetwo phase shifters include a phase modulator; and one or both of thecouplers includes a 2×2, 50/50 splitter.
 20. The polarization controllerof claim 12, wherein at least some portion of the polarizationcontroller is a photonic integrated circuit (PIC) constructed of siliconphotonics or indium phosphide.